Optimal Contact Tracing and Social Distancing Policies to Suppress a New Infectious Disease

Abstract

This paper studies the suppression of an infectious disease in the canonical SIR model. It derives three results. First, if technically feasible, the optimal response to a sufficiently small outbreak is halting transmissions instead of building up immunity through infections. Second, the crucial tradeoff is not between health and economic costs but between the intensity and duration of control measures. A simple formula of observables characterizes the optimum. Third, the total cost depends critically on the efficiency of contact tracing since it allows relaxing costly social distancing without increasing transmissions. A calibration to the COVID-19 pandemic illustrates the theoretical findings.